**Energy
storage in capacitors**

A capacitor is
capable of storing internal energy, due to charge begin moved
across the voltage difference. For moving a small charge *D**q* across a capacitor, the change in
potential energy is:

,

where *q* is the charge
already on the capacitor. As a capacitor is charged from *q=0*,
the first charges come on to the capacitor while it
has little charge, and hence do little to the internal energy;
while the last charges surmount the entire final voltage difference.
With a little calculus one can show:

All three equations for the
energy *U*, which are equivalent because *C = q/V*, will
be useful.